Lecture 06 Wireless Communication I-Hsiang Wang ihwang@ntu.edu.tw - - PowerPoint PPT Presentation

Lecture 06 Wireless Communication

I-Hsiang Wang

ihwang@ntu.edu.tw National Taiwan University 2017/12/27 Principle of Communications, Fall 2017

Recap

• Lecture 05 explored wideband communications over wires
• Point-to-point communication: single Tx/Rx pair
• Physical modeling:
• Noise modeled as additive white Gaussian noise
• Frequency selectivity modeled as convolution with LTI filter
• End-to-end equivalent discrete-time complex baseband channel
• Techniques developed:
• Optimal detection principles at receiver (Lecture 03)
• Error-correction coding to achieve reliable communication in the

presence of noise (Lecture 04)

• Interference mitigation techniques to combat inter-symbol interference

(Lecture 05)

• Key feature: channel is quite static and stationary over time.

2

Wireless Communication

• Wireless is a shared medium, inherently different from wireline
• More than one pairs of Tx/Rx can share the same wireless medium
• ⟹ can support more users, but also more interference
• Signals: broadcast at Tx, superimposed at Rx
• ⟹ more paths from Tx to Rx (variation over frequency)
• Mobility of Tx and Rx
• ⟹ channel variation over time
• Fading: the scale of variation over time and frequency matters
• Key challenges: interference and fading
• Look at point-to-point communication and focus on fading
• Where does fading come from?
• How to combat fading?

3

Outline

• Modeling of wireless channels
• Physical modeling
• Time and frequency coherence
• Statistical modeling
• Fading and diversity
• Impact of fading on signal detection
• Diversity techniques

4

5

Part I. Modeling Wireless Channels

Physical Models; Equivalent Complex Baseband Discrete-Time Models; Stochastic Models

6

Multi-Path Physical Model

Signals are transmitted using EM waves at a certain frequency Far-field assumption: Tx-Rx distance λc

c fc

fc

speed of light

Approximate EM signals as rays under the far-field assumption. Each path corresponds to a ray. The input-output model of the wireless channel (neglect noise) y(t) = X

i

ai(t)x (t − τi(t))

7

For path i : y(t) = X

i

ai(t)x (t − τi(t)) ai(t): channel gain (attenuation) of path i τi(t): propagation delay of path i Simplest example: single line-of-sight (LOS) r x(t) a(t) = α r (free space); τ(t) = r c y(t) = α

r x(t − r c)

8

y(t) = X

i

ai(t)x (t − τi(t)) Example: single LOS with a reflecting wall

d r

Path 1: a1(t) = α

r ;

τ1(t) = r

c

Path 2: a2(t) = −

α 2d−r;

τ2(t) = 2d−r

c

a2(t) = −

α 2d−r0−vt;

τ2(t) = 2d−r0−vt

c

a1(t) =

α r0+vt;

τ1(t) = r0+vt

c

r(t) = r0 + vt

9

y(t) = X

i

ai(t)x (t − τi(t)) Example: single LOS with a reflecting wall and moving Rx

d

Path 1: Path 2:

v

10

Linear Time Varying Channel Model

Impulse response: Frequency response: h(τ; t) = X

i

ai(t)δ (τ − τi(t)) ˘ h(f; t) = X

i

ai(t)e−j2πfτi(t) h (τ; t) x(t) y(t) = X

i

ai(t)x (t − τi(t)) Equivalent baseband model can be derived, similar to the derivation in wireline communication

Continuous-Time Baseband Model

11

xb(t) hb (τ; t) yb(t) = X

i

ab

i(t)xb (t − τi(t))

Impulse response: hb(τ; t) = h(τ; t)e−j2πfcτ = X

i

ab

i(t)δ (τ − τi(t))

Frequency response:

ab

i(t) , ai(t)e−j2πfcτi(t)

˘ hb(f; t) = ˘ h(f + fc; t) The gain of each path is rotated with a phase

Discrete-Time Baseband Model

12

vm = X

l

hl[m]um−l hl[m] um Impulse response: h`[m] , Z ∞

−∞

hb(⌧; mT)g(`T − ⌧) d⌧ = X

i

ab

i(mT)g(`T − ⌧i(mT))

Recall: examples: sinc pulse, raised cosine pulse, etc. g(t) is the pulse used in pulse shaping Observation: The `-th tap h`[m] majorly consists of the aggregation of paths with delay lying inside the “delay bin” ⌧i(mT) ∈ ⇥ `T − T

2 , `T + T 2

⇤

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delay

T 2T 3T

τ1 τ2 τ3τ4 τ5 τ6 τ7 τ8

14

delay

T 2T 3T

τ1 τ2 τ3τ4 τ5 τ6 τ7 τ8

ℓ = 0

15

delay

T 2T 3T

τ1 τ2 τ3τ4 τ5 τ6 τ7 τ8

ℓ = 1

16

delay

T 2T 3T

τ1 τ2 τ3τ4 τ5 τ6 τ7 τ8

ℓ = 2

17

delay

T 2T 3T

τ1 τ2 τ3τ4 τ5 τ6 τ7 τ8

ℓ = 3